Oct-doku

For fans of Killer Sudoku, Samurai Sudoku and other variants

Postby gsf » Thu Sep 11, 2008 12:22 pm

I went through the current catalog of 47909 17s
and derived all essentially different minimal octdokus
here are the counts per number of clues
Code: Select all
   507 22
 55336 23
101245 24
 37816 25
   382 26
gsf
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Location: NJ USA

Postby coloin » Thu Sep 11, 2008 1:58 pm

gsf wrote:
Code: Select all
   507 22
 55336 23


I will take stock of these findings ..........

Its not so easy to move from one puzzle to another.

the improvement from

nine less clue positions
one less clue value
three less clues........................... isnt quite enough.

Im thinking there must be equivalent clues, but how many......[obviously keep the 9]

Maybe there will always be 3 [equiv] clues.

Will see.

Thanks for your effort

C
coloin
 
Posts: 1633
Joined: 05 May 2005

Postby coloin » Fri Sep 12, 2008 1:27 pm

OK.... a little bit of thought.

What we are trying to do is generate these 14-plus-9 octdoku/vanilla sudoku puzzles.

For a long while we have randomly made new 17-puzzles and they are still being found. Can we get them all ?

By making these oct-duku puzzles with 14 clues we can very easily search for a 17. Almost all 17s have 3 of one particular clue value.

It has to be easier making these 14 octuku puzzles. [3 less clues, 9 less spaces and 1 less clue value]

gsf has made and canicalized the 13-plus-9 and 14-plus-9 puzzles from gordons list.

We can also get these puzzles from these here -
[18-puzzles with a 14 plus 4 configuration] [********4]
[19-puzzles with a 14 plus 5 configuration] [********5]
[20-puzzles with a 14 plus 6 configuration] [********6][?exists]

they are not common compared to other puzzles with n-clues.

These all do exist. - If you take a 17-puzzle with a diagonal pattern of the same clue value eg in B1B5B9 - replacing these 3 clues of the 9 rookery with the other 6 always gives a non-minimal puzzle and sometimes gives a 20-clue minimal puzzle with [********6]

We shouldnt attempt the 14-plus-9s untill we improved our method, and perhaps not before we can show we have all the 13-plus-9 octdoku.

These will all come from the 18-puzzles with [********5] distribution

optimization

It cant be wrong to fix one clue.
It cant be wrong to always be able to find a "gap" in a puzzle.

I believe all puzzles must have a clue like the 1 at r1c7 [not proven]
ie there is a box like
Code: Select all
+---+
|1**|
|...|
|9..|
+---+

maybe this can be improved on.
Code: Select all
+---+---+---+
|9**|***|1**|
|...|9..|...|
|...|...|9..|
+---+---+---+
|.9.|...|...|
|...|.9.|...|
|...|...|.9.|
+---+---+---+
|..9|...|...|
|...|..9|...|
|...|...|..9|
+---+---+---+

always pick all the 9s
always pick the 1 at r1c7 and
never pick any of the clues in r1c2-r1c6 and r1c8 and r1c9
Code: Select all
+---+---+---+
|987|654|123|
|...|9..|...|
|...|...|9..|
+---+---+---+
|.9.|...|...|
|...|.9.|...|
|...|...|.9.|
+---+---+---+
|..9|...|...|
|...|..9|...|
|...|...|..9|
+---+---+---+


In the two types of 18-puzzles I found at random - those with [011222235] and those with [011122335]

In both we "only" have to iterate 12 clues with 7 clue values over ~ 55 positions each. [still too much]

For now I will look at the incidence and configuration of possible
[********5]&[********4] for the 18s
[********5] for the 19s
[********6] for the 20s and poss 19s

C
coloin
 
Posts: 1633
Joined: 05 May 2005

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